[Haskell-cafe] Closures in Haskell and closures in set theory

If I'm not mistaken, in set theory, a closure of R with respect to some property P is the smallest superset R* that has the property P. To me, intuitively, a closure C in programming languages is a function that has bindings to variables declared in "parent" functions; so the inner function can not exist on its own, it needs a "parent environment". This seems to be related to set theory if we define R as the set of parameters of C, and R* as this set extended with the "parent variables" to which C binds, and P as the property "C can be evaluated". Does this make any sense at all?